Up to a quarter of school trips will be cut over the next year because of new government rules on teacher absence, headteachers have warned.

From 1 September, state primary and secondary teachers in England and Wales will be expected to cover for their absent colleagues only "rarely".

What the wording means has yet to be decided, but a teachers' union is pushing for it to be defined as "only in exceptional circumstances, such as emergencies".

The National Association of Head Teachers (NAHT) told the Guardian up to a quarter of all school trips would be axed as a result of the rule, regardless of its precise definition. Schools do not have the money to pay between £150 and £200 a day for an agency supply teacher to cover for teachers away on trips, heads argue.

Teaching unions, employers and the government signed a pact in 2003 known as the national agreement. One of its aims was for teachers to rarely cover for absent colleagues. It was agreed that cover was not a good use of teachers' time.

The Department for Children, Schools and Families said that schools would be expected to implement this from next term.

Under the same agreement, teachers have been relieved of administrative duties such as collecting dinner money and invigilating exams.

Latest figures from the government's Office of Manpower Economics show that a secondary school teacher on average covers for absent colleagues for 22.8 hours each year. Headteachers estimate that 60% of cover is needed because of teachers being away on school trips or training courses.

They said they relied on teachers' goodwill to step in when a colleague wanted a day off for their child's graduation or for the funeral of a relative, for example, but that this may now not be possible.

The rare cover rule comes almost a year after the schools secretary, Ed Balls, launched an "Out and About" scheme to give schools clearer information to help them organise learning outside the classroom.

At the time, Balls said: "Trips and getting out of the classroom should be part and parcel of school life and always give the most vivid childhood memories."

Chris Howard, president of the NAHT and headteacher of Lewis school Pengam, in Caerphilly, Mid Glamorgan, said: "Schools will almost certainly have an increase in cover-teaching costs and will reduce the number of trips they take pupils on by an estimated 20% to 25%. The teaching unions will say that if a school plans ahead, it will be able to cater for this, but schools can't plan that much ahead. Opportunities come up in the year.

"If rare cover comes to mean no cover or only a few lessons per year, there are going to be many occasions when heads will have to bring in supply staff, and they won't be able to afford that.

We all agree that teachers' time is spent more effectively not doing cover supply, but there are significant concerns about this."

Tracy Campbell, headteacher of Plantsbrook school in Sutton Coldfield, West Midlands, said her school was likely to cut at least 25% of its 100 trips each year. Uuniversity open days would be among the casualties, she said. "Universities phone us to say it's their open day next week and why don't we send a few sixth formers. Obviously the sixth formers need to be accompanied. We will have to say no," she said.

Campbell said a regular week-long trip to France for 13- and 14-year-olds would now be squeezed into a long weekend.

Geoff Barton, headteacher of King Edward VI school in Bury St Edmunds, Suffolk, said 25% of the 69 trips his pupils go on each year would be cut. Among last year's trips were a lecture at Cambridge University, a choir trip to Spain and an afternoon play. He said administrators, parents or teaching assistants accompany pupils on trips.

"This is chiefly because supply cover costs us £200 a day making the cost of covering so many trips extortionate," said Barton. "The things that make school life special and memorable are often those that lie beyond the classroom. Trips are a chance for teachers to help pupils to relate what they have seen in the wider world to what they have learned in class. This new rule is causing quite a lot of disquiet among many teachers."

But Chris Keates, general secretary of the NASUWT teaching union, said she was pressing for rare cover to mean "cover only in a major emergency that is so rare it could not have been foreseen".

She said it was "absolute nonsense" to suggest school trips would have to be cut. "Schools need a robust system and to plan ahead," she said. She suggested schools use support staff, pay for cover supervisors and could share lists of cover teachers. SheKeates said the new rule freed up teachers "to concentrate on teaching and learning".

A spokeswoman from the DCSF said: "There is absolutely no reason why schools should stop providing school trips because of the rarely-cover provisions. Schools trips should be an integral part of every child's education and personal development and provision for them should be included in school calendars and timetables. Appropriate arrangements should be made for both the staff and pupils who will be taking part in the trip and for those who are not."